Abstrakt:
I will describe a class of quasigroups obtained from directed triple systems. Their construction is similar to that of Steiner quasigroups from Steiner triple systems. Indeed commutative DTS-quasigroups are Steiner quasigroups. However in general their properties differ from those of Steiner quasigroups in certain important respects. I will discuss these and present a number of existence results. There remain many unsolved problems in this area. This is joint work with Ales Drapal and Andrew Kozlik.

Abstrakt:
The algebraic translation of the Dichotomy conjecture for
complexity of constraint satisfaction problem has received a lot of
attention in recent years. As a result, quite a few advances have been
achieved, and hopes are high in the community of universal algebra that
our area will manage to resolve this important conjecture of complexity
theory. We will introduce the problem, mention a few related results and
a related conjecture. Then we will turn our attention to the congruence
distributive case, place it in the overall picture of efforts towards
resolution of the Conjecture, review the partial results which are known
and the problems which are left to be resolved.

Abstrakt:
A map from a group G to itself is called polynomial if it can be written
as a product consisting of constant functions, the identity, and the
function g --> g^{-1}. We discuss several concepts related to
polynomiality on linear groups. Furthermore we give a necessary
topological condition for a map to be polynomial. As a consequence we
prove that transposition is in general not polynomial.

Abstrakt:
We generalize an old result of J. Ježek and T. Kepka that any medial
groupoid without irreducible elements is a subreduct of a certain
semimodule over commutative semiring. Namely we prove that any
semibly entropic algebra without irreducible elements is a
subreduct of a semimodule over commutative semiring. Next we use
our theorem to show that any cancellative entropic algebra is a
subreduct of a module over commutative semiring.

Abstract:
In recent years, algebraic cryptosystems, especially cryptosystems based on combinatorial group theory,
experienced a considerable increase in active interest. We connect classical computational problems in
group theory to corresponding problems in monoid and group rings and free modules over monoid rings and
show how these problems can be solved if one succeeds in computing a Gröbner basis. We then introduce a
new class of Gröbner basis cryptosystems.

Abstract:
An AFL (Abstract Family of Languages) (a full AFL, resp.)
is a language family closed under nonerasing morphism (arbitrary morphism,
resp.), inverse morphism, intersection with regular sets, union,
concatenation and catenation closure. The basic theme of the talk will be:
how simple can a one letter language be and still generate (using the full
AFL operations and intersection) all recursively ennumerable languages. The
problem is old, some new partial results have been obtained recently.